Periodic functions with variable period – basic concepts and certain investigation results
| Назва | Periodic functions with variable period – basic concepts and certain investigation results |
| Назва англійською | Periodic functions with variable period – basic concepts and certain investigation results |
| Автори | Mykola Pryimak |
| Принадлежність | Ternopil Ivan Puluj National Technical University, Ternopil, Ukraine |
| Бібліографічний опис | Periodic functions with variable period – basic concepts and certain investigation results / Mykola Pryimak // Scientific Journal of TNTU. — Tern.: TNTU, 2024. — Vol 113. — No 1. — P. 46–57. |
| Bibliographic description: | Pryimak M. (2024) Periodic functions with variable period – basic concepts and certain investigation results. Scientific Journal of TNTU (Tern.), vol 113, no 1, pp. 46–57. |
| DOI: | https://doi.org/10.33108/visnyk_tntu2024.01.046 |
| УДК | 517.51 |
| Ключові слова | periodic functions with variable period, variable period, trigonometric functions with variable period. |
Investigation of real signals is one of the most important applied areas of mathematics. According to their properties, signals are quite diverse, and methods of their research are different as well. Among this diversity, periodic signals with variable period make up a significant proportion. Till present, no attention was paid to the theory of such signals. In this paper, we define periodic functions with variable period, which are the model of these signals. Some properties of the variable period are considered. Examples of the analytical formulation of functions with variable period in the form of trigonometric functions with variable period are given and their variable periods are recorded. It is pointed out that these functions can be used as basic ones for constructing orthogonal system of trigonometric functions with variable period and its use for constructing Fourier series of functions with variable period. | |
| ISSN: | 2522-4433 |
| Перелік літератури |
1. Pryimak M. V., Bodnarchuk I. O., Lupenko S. A. Umovno periodychni vypadkovi protsesy iz zminnym periodom. Visnyk Ternopilskoho derzhavnoho tekhnichnoho universytetu. 2005. T. 10. No. 2. P. 132–141.
2. Pryimak M. V. Zminni periody deiakykh periodychnykh funktsii iz zminnym periodom: materialy KhI nauk. konf.Ternopilskoho derzhavnoho tekhnichnoho universytetu imeni Ivana Puliuia. Ternopil: vyd. TDTU, 2007. P. 71.
3. Pryimak M. V. Ortohonalni systemy periodychnykh funktsii iz zminnym periodom. Tam zhe. P. 72.
4. Pryimak M. V. Funktsii iz zminnym periodom. Visnyk Kyivskoho natsionalnoho universytetu imeni Tarasa Shevchenka. Matematyka, mekhanika. Vol. 2 (36). 2016. P. 14–16.
5. Bernshtein S. N. Ystorycheskyi obzor razvytyia poniatyia funktsyy. Vestnyk opиtnoi fyzyky y эlementarnoi matematyky. 1912. No. 559. Sem. 47. P. 177–184.
6. Luzyn N. N. Funktsyia (v matematyke). Matem. obr. 2005. Vol. 2. P. 37–42.
7. Shylov H. E. Chto takoe funktsyia? Matematyka v shkole. Metodycheskyi zhurnal mynysterstva prosveshchenyia RSFSR. 1964. No. 1. P. 7–15.
8. Fykhtenholts H. M. Osnovи matematycheskoho analyza. Tom 2. M.: Nauka, 1968. P. 424–433.
9. Stepanov V. V. Kurs dyfferentsyalnиkh uravnenyi. M.: Hos. yzd. f.-m. lyteraturи, 1959. P. 440–441.
10. Tiulyna A. K. Ob odnoi rukopysy neyzvestnoho avtora (k byohrafyy N. N. Luzyna). Ystorykomatematycheskye yssledovanyia. Vtoraia seryia. Vol. 11 (46). 2006. P. 267–306.
11. Pryvalov Y. Y. Riadи Fure. M.-L.: Hosyzdat, 1931. P. 164.
12. Bary N. K. Tryhonometrycheskye riadи. M.: Hos. yzd. f.-m. lyt., 1961. 936 p.
13. Stepanets A. Y. Klassyfykatsyia y pryblyzhenye peryodycheskykh funktsyi. Kyev: Nauk. Dumka, 1987. 268 p.
14. Honorovskyi Y. S. Radyotekhnycheskye tsepy y syhnalи. M.: Radyo y sviaz, 1986. 512 p. |
| References: |
1. Pryimak M. V., Bodnarchuk I. O., Lupenko S. A. Umovno periodychni vypadkovi protsesy iz zminnym periodom. Visnyk Ternopilskoho derzhavnoho tekhnichnoho universytetu. 2005. T. 10. No. 2. P. 132–141.
2. Pryimak M. V. Zminni periody deiakykh periodychnykh funktsii iz zminnym periodom: materialy KhI nauk. konf.Ternopilskoho derzhavnoho tekhnichnoho universytetu imeni Ivana Puliuia. Ternopil: vyd. TDTU, 2007. P. 71.
3. Pryimak M. V. Ortohonalni systemy periodychnykh funktsii iz zminnym periodom. Tam zhe. P. 72.
4. Pryimak M. V. Funktsii iz zminnym periodom. Visnyk Kyivskoho natsionalnoho universytetu imeni Tarasa Shevchenka. Matematyka, mekhanika. Vol. 2 (36). 2016. P. 14–16.
5. Bernshtein S. N. Ystorycheskyi obzor razvytyia poniatyia funktsyy. Vestnyk opиtnoi fyzyky y эlementarnoi matematyky. 1912. No. 559. Sem. 47. P. 177–184.
6. Luzyn N. N. Funktsyia (v matematyke). Matem. obr. 2005. Vol. 2. P. 37–42.
7. Shylov H. E. Chto takoe funktsyia? Matematyka v shkole. Metodycheskyi zhurnal mynysterstva prosveshchenyia RSFSR. 1964. No. 1. P. 7–15.
8. Fykhtenholts H. M. Osnovи matematycheskoho analyza. Tom 2. M.: Nauka, 1968. P. 424–433.
9. Stepanov V. V. Kurs dyfferentsyalnиkh uravnenyi. M.: Hos. yzd. f.-m. lyteraturи, 1959. P. 440–441.
10. Tiulyna A. K. Ob odnoi rukopysy neyzvestnoho avtora (k byohrafyy N. N. Luzyna). Ystorykomatematycheskye yssledovanyia. Vtoraia seryia. Vol. 11 (46). 2006. P. 267–306.
11. Pryvalov Y. Y. Riadи Fure. M.-L.: Hosyzdat, 1931. P. 164.
12. Bary N. K. Tryhonometrycheskye riadи. M.: Hos. yzd. f.-m. lyt., 1961. 936 p.
13. Stepanets A. Y. Klassyfykatsyia y pryblyzhenye peryodycheskykh funktsyi. Kyev: Nauk. Dumka, 1987. 268 p.
14. Honorovskyi Y. S. Radyotekhnycheskye tsepy y syhnalи. M.: Radyo y sviaz, 1986. 512 p. |
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